Repeated subdivides are not in single direction
Hmm. I did some testing. That video tutorial is from 2013 so the creater of that tutorial must have most likely been using blender 2.61 or 2.62 or 2.63 as that was the latest at that point of time.

When I downloaded and ran blender 2.61 the subdivide behaved like it did in the video. So this implies that something changed in blender since 2013. Since 2013 a lot has changed.

The subdivide behaviour you get now is the correct behaviour as per the latest blender. The older blender subdivided in one direction.

I would advice you use edge loops like suggested by  Dontwalk earlier i.e. with Ctrl + R shortcut to slice in one direction.

Alternatively download and use blender 2.61/2.62/2.63 to follow along with that tutorial.

Older versions of blender can be obtained here https://download.blender.org/release/. The date of release of those blender versions is also mentioned there. (Note: these versions are no longer supported -- use at own risk).